Article ID Journal Published Year Pages File Type
4673153 Indagationes Mathematicae 2013 12 Pages PDF
Abstract
Let (Ω,Σ,μ) be a finite complete measure space and (X,‖⋅‖X) be a Banach space with the Banach dual X∗. Let L∞(μ,X) denote the space of all μ-measurable functions f:Ω→X such that esssupω∈Ω‖f(ω)‖X<∞. We study the problem of the integral representation of some natural classes of linear operators from L∞(μ,X) to a Banach space with respect to the corresponding operator measures. We characterize relatively σ(bvcaμ(Σ,X∗),L∞(μ,X))-sequentially compact sets in the space bvcaμ(Σ,X∗) of all countably additive measures ν:Σ→X∗ of bounded variation with ν(A)=0 if μ(A)=0.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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